Question

In: Math

Average Total Payments $7,605.44 $7,861.23 $7,291.77 $7,264.79 $7,537.16 $8,010.86 $7,316.82 $7,421.40 $8,594.81 $6,993.72 $6,905.37 $6,832.44 $7,015.00...

Average Total Payments
$7,605.44
$7,861.23
$7,291.77
$7,264.79
$7,537.16
$8,010.86
$7,316.82
$7,421.40
$8,594.81
$6,993.72
$6,905.37
$6,832.44
$7,015.00
$7,394.07
$7,054.60
$7,491.51
$7,504.30
$8,663.12
$10,985.44
$7,482.67
$7,676.57
$6,884.62
$7,440.25
$7,421.67
$9,764.10
$7,107.36
$7,728.79
$11,497.33
$8,713.97
$8,621.84
$7,726.40
$6,679.73
$7,066.34
$13,435.10
$6,912.62
$7,526.55
$8,441.81
$6,787.02
$8,633.87
$6,812.10
$6,881.70
$8,568.06
$7,648.96
$7,954.37
$8,031.93
$8,091.48
$6,860.73
$7,100.69
$7,197.31
$7,703.08
$7,185.20
$7,321.56
$8,528.78
$10,414.00
$6,489.25
$7,218.42
$6,646.68
$7,577.64
$8,419.36
$7,135.96
$7,495.96
$7,485.07
$6,884.68
$7,941.81
$8,122.57
$7,944.23
$8,175.08
$8,014.70
$7,603.22
$7,408.60
$7,737.51
$8,373.15
$7,349.52
$7,928.17
$7,268.87
$8,167.19
$6,547.92
$7,005.88
$6,885.49
$6,726.93
$6,607.64
$6,681.15

What percentage of Average Total Payments is less than $7,000?

What percentage of Average Total Payments should be less than $7,000 based upon the mean and standard deviation?

What percentage of Average Total Payments is less than $10,000?

What percentage of Average Total Payments should be less than $10,000 based upon the mean and standard deviation?

Please show how the answer was calculated.

Expert Solution

First we need to calculate the mean and SD of data set. Following table shows the calculations:

	X	(X-mean)^2
	7605.44	14251.05913
	7861.23	18608.28831
	7291.77	187530.3971
	7264.79	211625.5768
	7537.16	35215.4499
	8010.86	81820.14018
	7316.82	166462.2048
	7421.40	92062.36136
	8594.81	756886.4281
	6993.72	534503.9932
	6905.37	671494.6969
	6832.44	796338.1379
	7015.00	503841.3092
	7394.07	109394.1072
	7054.60	449191.8994
	7491.51	54432.52954
	7504.30	48628.10012
	8663.12	880411.0185
	10985.44	10631657.13
	7482.67	58635.55704
	7676.57	2327.850205
	6884.62	705932.3431
	7440.25	80978.8328
	7421.67	91898.58864
	9764.10	4158671.891
	7107.36	381254.1348
	7728.79	15.77837284
	11497.33	14231848.3
	8713.97	978422.0748
	8621.84	804648.8273
	7726.40	2.50335684
	6679.73	1092208.51
	7066.34	433593.0131
	13435.10	32607322.8
	6912.62	659665.2663
	7526.55	39310.12052
	8441.81	514077.8149
	6787.02	879464.7137
	8633.87	826375.9023
	6812.10	833053.7824
	6881.70	710847.6247
	8568.06	711057.4079
	7648.96	5754.405821
	7954.37	52694.21252
	8031.93	94317.90339
	8091.48	134441.1689
	6860.73	746647.7261
	7100.69	389535.5107
	7197.31	278264.4791
	7703.08	472.5319488
	7185.20	291187.3701
	7321.56	162616.8533
	8528.78	646355.219
	10414.00	7231700.905
	6489.25	1526627.788
	7218.42	256438.7318
	6646.68	1162381.116
	7577.64	21661.30481
	8419.36	482388.8676
	7135.96	346753.5086
	7495.96	52375.89262
	7485.07	57479.0076
	6884.68	705831.523
	7941.81	47085.61486
	8122.57	158206.8126
	7944.23	48141.71351
	8175.08	202736.0487
	8014.70	84031.68988
	7603.22	14786.02496
	7408.60	99993.69704
	7737.51	161.0919408
	8373.15	420334.6416
	7349.52	140848.4387
	7928.17	41352.11724
	7268.87	207888.3963
	8167.19	195693.1633
	6547.92	1385088.432
	7005.88	516871.5603
	6885.49	704471.1559
	6726.93	995780.0614
	6607.64	1248086.237
	6681.15	1089242.477
Total	633435.06	99292693.87

----------------------------

Out of 82 values, 18 are less than 7000 so the percentage of Average Total Payments is less than $7,000 is

(18*100) /82 = 21.95%

Answer: 21.95%

-------------------

The z-score for X = 7000 is

The percentage of Average Total Payments should be less than $7,000 based upon the mean and standard deviation is

P(X < 7000) = P(z < -0.65) = 0.2578

Answer: 25.78%

-------------------------------------

Out of 82 values, 78 are less than 10000 so the percentage of Average Total Payments is less than $10000 is

(78*100) /82 = 95.12%

Answer: 95.12%

-------------------

The z-score for X = 10000 is

The percentage of Average Total Payments should be less than $10,000 based upon the mean and standard deviation is

P(X < 10000) = P(z < 2.05) = 0.9798

Answer: 97.98%

milcah answered 8 months ago

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